When a dog rips there nail off it does leave that 'quick' (a bed of blood vessels and nerves) region exposed. This bit of tissue can bleed quite a bit and can be quite sore with that exposed nerve.

You haven't mentioned that she has had any bleeding, but if she does you can dab on cornstarch (aka cornflour) to staunch any bleeding. Then as long as its clean and she will let you, the best thing to do is make sure it is clean an then bandage it so she doesn't bang it and hurt herself more.

The quick itself will dry/shrivel up and the nail will regrow. There is no need for the quick itself to be removed. The only concern is whether the nail was a complete and clean removal or not.

If she has pulled it completely off, then you are on the right track. Cleaning, bandaging and monitoring is exactly what we would do. The bandage should be put on reasonably tight, but make sure its not so tight that blood flow is compromised.

If there is some nail remaining, she will need to have the remaining removed (under sedation) at the vets.

This can be quite sore, but remember dogs cannot metabolize human pain medications, so these should not be given. If you have some metacam or rimadyl on hand, she can have her prescribed dose. This will help with the discomfort.

Please let me know if i can provide any further information or if you need any further help.